Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field

Abstract

We examine a family ₚ𝐺ᶜq[⁽ᵃ⁾₍b₎; 𝔃] of integrals of Mellin-Barnes type over the space ℤ × ℝ, such that functions 𝐺 naturally arise in the representation theory of the Lorentz group. We express ₚ𝐺ᶜq(𝔃) as quadratic expressions in the generalized hypergeometric functions ₚFq₋₁ and discuss further properties of the functions ₚ𝐺ᶜq(𝔃).